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A fluid of density rho flows through a h...

A fluid of density `rho` flows through a horizontal pipe having two different cross-section s of areas A and 2A, Th e pressure at the smaller cross-section is P and lluid velocity at that section is v· What is the velocity and pressure at the larger cross-sect ion

A

`v/2,P+1/2rhov^2`

B

`v/4,P+3/8rhov^2`

C

`v/2,P+3/8rhov^2`

D

`v,P+3/4rhov^2`

Text Solution

Verified by Experts

The correct Answer is:
B
From the equation of continuity, Av=A'v'
Where A'=2A `:.` Av=2Av'
`:.` v'=`v/2`
According to Bernouli's theorem, for the horizontal pipe,
`P+1/2rhov^2=P'+1/2rho[v^2-v^('2)]`
`=P+1/2rho[v^2-(v^2)/(4)]=P+1/2rho((3v^2)/(4))`
`:." "P'=P+3/8rhov^2`
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